How does one conduct background checks on a person via Google?

just look them up - depending on how common the name is and the amount
of information available you'll have varying degrees of success.

If for example you were Mike Michelson
://www.google.com/search?num=50&hl=en&ie=UTF-8&oe=UTF-8&safe=off&q=%22mike+michelson%22&spell=1
gives you quite a bit of info - real gems are if you can find online
cv or pictures or something like that...
If you mean official background checks (criminal record etc) then as
far as I know you can't do it through Google though there are likely
to be links to a third party that could provide that sort of info.

Google can help you two ways on running a background check. The first
one is to type the persons name in the google search engine. Try it
with and without quotes around the persons name. Example. John Doe and
"John Doe".
Please note that the above way may or may not return information on
the subject. Even if the search results turn up some information on
your subject it is still not a complete background check.
The second way is to enter the word background checks in the google
search box. You will get over 3,000,000 hits on different companies
selling what they call background checks. I recommend the company
below. They have been in business since 1986.

If you want a complete background check done you can always use a
company called The Pros Investigative Service And Spy Gadgets. They
can run nationwide and international criminal background checks. They
also sell surveillance products, Below is some information on The
Pros.

Information retrieval for insurance companies, law firms, repossession
agents, financial institutions, collection agencies, private
investigators, bounty hunters, process servers, bail bondsmen,
businesses, spouses and parents.

Offering nationwide and international investigative services, covert
spy gadgets, safety and surveillance products, records research,
Unmanned Aerial Surveillance Vehicles, UAV, criminal records
background checks, listed and unlisted phone number searches, cellular
phone searches and records, cellular phone locating, pager cloning,
nationwide wants and warrant searches, sex offender search, Biometric
security products, keyspy keystroke recorders, email / Instant
Messenger/ IP address searches, DMV searches, skiptracing, deadbeat
parent and people finder searches, personal information verification
services and much more.
The below web address will bring you to The Pros web strore.
http://www.ioffer.com/selling/infopros